The short version is no, they didn’t really, at least not during the Middle Ages (I can’t vouch for earlier, not my area). The medieval battlefield wasn’t particularly well suited to long ranged precision archery – once everyone was in a melee there wasn’t much opportunity to engage in specific targeted shooting without a huge risk of friendly fire. Archers in fact would often be armed with melee weapons of their own and might join in the fight once things got particularly intimate, leaving their shooting to either covering the advance of the army, forcing a repositioning or disadvantageous attack by enemy forces, or covering a retreating force (although retreating in good order wasn’t particularly common in the Middle Ages so this was probably the rarest of all). In essence they were more of a support weapon than one suited to specific deadly killing – despite what some in the longbow-fandom might have you believe.

As for assassinations, that raises a more interesting question. I’m going to limit my answer a bit by focusing on the crossbow because it’s arguably the weapon better suited to this task. The crossbow was generally more accurate, much easier to aim, and had the advantage of being able to be loaded held ready while the archer lined up the perfect shot (in theory anyway). The crossbow was also used in a few famous assassinations and assassination attempts, a few of which I’m going to discuss below.

Probably the most famous person ever to be killed by a crossbow is King Richard I of England. On the twenty-fifth of March 1199, King Richard I of England decided to patrol the walls of the Château de Châlus-Chabrol. He had been besieging the castle for some time and he may have decided that evening to inspect the progress of his sappers in their attempts to breach the castle’s defences, we can’t know for certain. Whatever his reason he very quickly would come to regret his decision as that evening he was shot by a crossbow wielded by one of the castle’s defenders. Richard was transported back to his private tent, where the crossbow bolt was removed a process which, thanks to the dubious qualities of medieval medicine, badly mangled his arm. The wound soon became gangrenous. While the king lay dying in his camp his forces successfully completed the siege and put the defenders to the sword. Richard died on the sixth of April, just over a week after he had been initially wounded. His heart and entrails were buried in the castle’s chapel and his body was transported Fontevraud Abbey in Anjou, where his father had been buried almost a decade earlier.

While King Richard has left us nothing in terms of a description of how he came to be mortally wounded the same cannot be said for contemporary historians. There are numerous accounts of the death of King Richard I – after all a king dying in a battle or siege was a fairly rare event even in the Middle Ages– from which we should be able to reconstruct the events of his death in greater detail. Unfortunately for historians, these accounts often disagree on major details and are often filled with errors – making constructing a single coherent narrative of the death of the king a difficult task. There are many interesting things to be learned from these accounts, though, and it is worth spending a time here exploring a few of the more interesting and informative ones.

Remarking on his death, the French chronicler William le Breton found a certain poetic irony to his fatal wounding by the crossbow, as he accused the vile Richard of having introduced this most sinful weapon to European warfare in the first place, making it only fitting that it be the tool to relieve Europe of his presence. This theory for the origins of the crossbow is patently false. The crossbow, along with the bow, had been banned in inter-Christian warfare at the Second Lateran Council in 1139, nearly twenty years before Richard was born. The ban obviously was not very effective, Richard’s death is a pretty clear testimony to that, but the Lateran ban adds further confusion to the French chronicler’s statement. It seems unlikely that he would be entirely ignorant of the decrees Council of a major papal council.

It is also interesting to note that this anecdote about Richard introducing the crossbow appears in only one of William le Breton’s two accounts of Richard I’s death. In William’s Gesta Philippi, a prose chronicle about the life of King Philip II, he nearly exactly copies the version of events presented in the work of Rigord, another French chronicler who was writing a few decades before William. Rigord’s account is not particularly in-depth and describes how Richard besieged the castle because he desired a recently discovered treasure – a treasure which Rigord describes as a golden figure of a Roman emperor – before he was shot and killed by an unknown crossbowmen.

It is in his Philippidos where William really lets his imagination run wild and the death of Richard I is a 200 line literary set piece that closes out Book V of this panegyric written to praise King Philip II of France in celebration of his victory at Bouvines in 1214. The relevant passage mentioned above comes as part of a 31-line speech delivered by one of the three Fates who has decided that while her sisters are still weaving Richard’s life she feels it must end. She guides Lord Archard of Chalus – the lord of the castle and person who we are told found the treasure in the first place – to discover a hidden crossbow bolt because: "This is how I want Richard to die, for it was he who first introduced the crossbow into France. Now let him suffer the fate he dealt out to others." This speech must be seen within the broader context of the work – the Philippidos is a work meant to praise Richard’s long-time rival Philip II and as part of that work it frequently and vehemently condemns the English king in no uncertain terms. We are told that Richard I was killed because of his greed in demanding the treasure for himself despite no claim to it, and that he had no respect for God, broke treaties, and violated holy days. No crime is beneath Richard in this work, and so the suggestion that he was responsible for introducing the crossbow is just another exaggerated crime of the English king.

The English chronicler Roger of Howden wrote what is probably the most famous account of Richard’s death and his confrontation with his killer. Roger of Howden was an English chronicler probably best known for accompanying Richard on the Third Crusade and providing a detailed account of the expedition. Roger tells us that Richard was outside Chalus Castle preparing for the imminent assault when he was shot by the crossbow, and upon being shot Richard rode back to camp and told the captain of his mercenaries to begin the assault without him. Roger tells us that Richard was shot by a man named Bertrannus de Gurdon and that when Richard learned that he would not survive he had Gurdon called before him – the castle having fallen by this stage and its defenders captured. We are told that Richard asked him: "What wrong have I done to you that you should kill me?" To which Gurdon responded: "You killed my father and my two brothers and you wished to kill me. Take what vengeance you like. So long as you die I shall willingly suffer any torments you may devise." Roger says that Richard forgave Gurdon and ordered him be released, but upon the king’s death the captain of his mercenaries, a man named Mercadier, had Gurdon captured and flayed alive. This narrative is probably the closest we come to having a clear assassin who was determined to specifically kill King Richard.

The historian John Gillingham has suggested there are reasons to doubt Roger’s account of events, however. While Roger has generally been regarded as an impartial and reliable source, Gillingham draws a distinction between what Roger was writing in the 1170s and 1180s from his work in the 1190s. While in his younger years Roger had been intimately involved in Anglo-French politics, by the late 1190s he had retired to Howden in Yorkshire and seems to have primarily concerned himself with regional matters in and around northern England. As such, he probably is not a particularly informed source about events in central France during this period. So while we know Roger was writing very close to the event – he only outlived Richard by a few years – Gillingham suggests there is reason to interpret the Bertrannus de Gurdon story as myth.

I wrote this as a response to a post about the atlatl which was deleted.

One thing to consider is why you would consider "stories of individual archers accomplishing such feats" as not fitting into the idea of a "sniper" given the way that that role arguably orientates itself towards individual feats of marksmanship (though over the course of the twentieth century it has increasingly become a paired role).

I'd argue that there's something to the idea that individual skill at marksmanship was a defining feature of the martial capacity of many less industrial/agricultural societies. The origin of the term itself is with the hunting of "snipes", a bird in the Indian subcontinent. A society that valued hunting often values marksmanship, and the flattened structure of such societies would in turn mean that disputes would often be understood in terms of individual antipathies (which would lead to the targeting of leaders) and asymetrical warfare over set-piece battles.

An example of this is the widespread use of a weapon commonly known elsewhere as the atlatl, amongst Aboriginal peoples in Australia. This was commonly used and in the Dharug language it was known as a "woomera": a long shaped piece of wood, ending in a hook, and sometimes doubling as a shield. One of the first representations of Aboriginal people shown in Europe has a warrior holding one (though through reproduction the artist represents it as a sort of club rather than a spear thrower).

I have personally seen a man from the Central Desert use one to great affect at what seemed like an extremely long distance, and they were widely used in resistance to European expansion from early on. The first Governor of the colony, Governor Arthur Phillip, was speared with one. David Collins description of that incident shows some of the skill with which it was deployed:

"(Willemering) …lifted a spear from the grass with his foot, and fixing it on his throwing-stick, in an instant darted it at the governor. The spear entered a little above the collar bone, and had been discharged with such force that the barb of it came through on the other side."

This incident apparently did not occur at range, but I recall at least one account lamenting the incapacity of muskets in comparison to the speed and accuracy of a skilled warrior using a woomera (a skill used not only in battle but also hunting animals like Kangaroos, which are not easy game).

So in this respect I guess it depends on how you define a "sniper". The resistance to the European invasion of Australia did not involve large set piece battles, but the spearing of Phillip shows that there were warriors who directly targeted colonial leadership (even if in this case the attack was likely retaliatory and "ritualistic", as being speared was a customary punishment for a range of breaches of communal norms, I recommend Inga Clendinnen's "Dances with Strangers" and Grace Karskens "the Colony" as starting points on this incident if anyone is interested).

So it's not quite an example of what the OP is asking about: "purpose-built military archery units", but it is an example of the tactical deployment of individual marksmanship skills in pursuit of strategic goals (targeting leadership, sowing terror etc.), which I'd argue is as good a definition of "sniping".

It's possible to reliably strike human sized targets at 100 yards or more with primitive archery tackle

It isn't.

I'll speak as someone who has dabbled in traditional archery and coach modern archery. Others have provided some historical accounts of notables being struck down by projectiles. There is largely a lack of historical evidence of a notable figure being purposefully hit by an arrow at long distance.

What exactly is a "sniper"?

In modern usage, a sniper refers to person armed with a precision weapon (typically a rifle) capable of engaging targets at extreme distances. There's also the extended understanding of a sniper in a military sense, being a scout and reconnaissance asset, as compared to a marksman, but that's a different discussion. In either case, a sniper is expected to engage targets beyond the normal combat range of other combatants (riflemen, machine guns, etc.)

At this point we have to appreciate the ranges that we can expect to see snipers being used as compared to other troops. Modern infantry combat takes place up to 200m with modern rifles. Snipers can expect to engage targets over 1000m away, with the record distances over 2000m (the longest confirmed kill being 3,540m) typically using high-calibre ammunition (such as .50) not used by regular infantry. In security contexts, marksmen (or police "snipers") would be expected to cover several hundred metres.

What's crucial to understand here the myth of archery accuracy. "Long range" for a bow, or a "bowshot", is around 150m, and this is a point where archers don't aim for specific targets but shoot indirectly (i.e. the "volley" that most are familiar with).

Modern snipers can function because they can, with extreme skill, training and with no small amount of arithmetic, guarantee that a bullet will hit a specific target hundreds of metres away. This is beyond what a person with a bow can do.

How far can an archer shoot accurately?

A modern competitive archer, using modern equipment (carbon arrows, sights, stabilisers, either recurve or compound), can hit a ~12cm spot at 70m (the size of the 'gold' 9/10 ring) about 95% of the time.

These are the world's best competitive athletes shooting in a sport that prioritises precision and consistency above all else, shooting in ideal conditions with impractical equipment. A more typical "elite" athlete might achieve about an 80% hit rate on that spot, while the average amateur club-level archer might be closer to 30-50%. The hit rate on the target will still be fairly high - you don't expect to miss the target once you've trained for the distance, but it's difficult to guarantee a hit on the centre unless you've honed your shooting skill over years.

(For those wondering, I'm basing these figures on world, national and club events and records. The sighted recurve men's record at 70m is 353/360, which means the archer hit the 9 ring seven times as opposed to the 10 ring).

In contrast, the Finals of the traditional division of the 2020 Conquest Cup, featuring Turkish archery shooting at a puta target [a human-sized pear-shape target] at 50m counting only hits, the winner achieved five out of nine hits; runner-up being three out of nine. Having shot with archers who are serious about this competition, five hits is good, seven is exceptional.

A 55% hit rate at 50m with somewhat equivalent equipment from historical periods isn't exactly "reliable".

Hunters, who need that single shot for a clean kill, typically shoot at much shorter distances, often under 30 metres. Compound shooters can engage further, but apart exceptional hunters such as Howard Hill, most traditional archers would not be confident shooting beyond 30 metres. Too many things can go wrong on release to guarantee the arrow hitting the kill zone.

On a side-note, battlefield archery was also known to be very short range for maximum effect. The archers at Agincourt, while capable of shooting over a hundred metres, mostly engaged the French knights at 25 metres or less. At this distance, this would be a "certain hit" most of the time with a war bow. On the other side of the world, Gao Ying's The Way of Archery - a Ming military manual - leans towards the reality that an archer should engage at close distance. To paraphrase, the idea is that they estimate their "certain hit" distance, and half that for the distance they should shoot.

The notion that historical archers, battlefield or otherwise, would be able to pick out a single target 100 metres away, is a romanticised ideal worthy of legend rather than a realistic application of a bowman. Realistically, the distances that a bow can accurately hit a target is so short, you may as well use a dagger.

Finally, so what if an archer could hit at that distance?

Arrows aren't bullets. A sniper can bring down a target with a high degree of lethality with the ammunition we have available, even more so if you're referring to .50 rounds. A shot to the head will likely kill, a shot to the torso will most likely cause a mortal wound. Arrows seldom kill instantly, the biggest threat being their removal and subsequent infection long after. Poison could work, but very few cultures made widespread use of poison, let alone for assassination purposes on arrow-heads.

In conclusion, you don't get archers to snipe high-profile targets or provide a security detail. The biggest threat isn't an arrow, but a dagger.

In Ancient Israel according to the biblical text,

there were seven hundred picked men who were left-handed; every one could sling a stone at a hair, and not miss. Judges 20:16, NRSV

It's rather an unusual thing. Biblically, the only people who are mentioned as being left-handed are in a military context^1, and there is absolutely some linguistic shenanigans going on because all of them are from the tribe of Benjamin - which means 'Son of my Right Hand', which goes to show that even God enjoys irony. But there appears to be no real benefit to being lefthanded in missile warfare so unless there is some other component that everybody is unaware of, it's a mystery (although see Eglon, where it absolutely was a Sneak Attack with a finesse weapon with critical (1d6+2d4), quite possibly on a toilet no less - eat your heart out Tyrion!). There is an indication in the text that these are elite soldiers, who are capable of giving their Israelite cousins a run for their money in the Israelite Civil War. It's only the hand of Yahweh which causes them to lose, but that's pretty much the only indication of what they did with those crack troops. There's no long distance slinging unless you count David vs Goliath, and there's not much indication of the distance.

^1 For those interested the others are Ehud, the slayer of Eglon, the Ancient Near Eastern 'Fat Bastard' of his day, and another group of soldiers in 1 Chronicles 12:2 who could shoot with either bow or sling with either their right or left hand.

Now that more than 12 hours have passed: all the answers address conventional individual weapons/archery and the like, but what about small artillery? Were small ballistae ("scorpions"?) able to achieve practical range and accuracy that bows/slings couldn't?